Solving word problems
There are many reasons why so many pupils find solving word problems difficult. For some, it is the amount and level of reading involved or the mathematical vocabulary that is a barrier to understanding. For others, it is an unfamiliar context in which they have no real-life experience, so they may quickly disregard the question.
But solving a problem is about understanding it and working out the steps involved to reach the answer, and this is where many pupils struggle to know where to begin. So, what can we do to help children learn how to solve word problems?
Research (Knapp, 2020) shows that most children only read a question once and skim over any charts, tables or diagrams, often ignoring labels and titles. Instead, many do what Hegarty (1995) describes as ‘number grabbing’ – making the numbers out of a question and throwing them into a calculation without full comprehension of what they are doing and why.
The difficulties lie in translating the word problem to a mathematical representation because pupils focus on the numbers rather than the information. Therefore, acronyms such as RUCSAC (read, underline, calculate, solve, answer, check) are not effective because of the huge conceptual jump from underlining to knowing what to calculate.
One of the things that I have been exploring in my classroom is the use of ‘goal free’ problems. These, as the name suggests, are word problems that include the information and numbers required but do not have the final ‘goal’ or question to solve. They are easily created for any year group, taking a question maybe from a SATs paper or bank of word problems and removing the question, usually found at the end. Most questions are suitable, including those
requiring single or multi-step solutions, those that involve reading charts or graphs and ones with a geometry concept.
Eliminating the ‘goal’ means that children no longer have to focus on finding an answer but instead focus on the information that they have in front of them, initiating valuable discussion opportunities.
Questions to ask the children could include:
what information does this give you?
what do you notice or wonder?
given this information, what questions could we answer? How do you know? How would you work that out?
what questions could we not answer? What extra information would we need to be able to answer that?
After modelling an example to the class, pupils can work in pairs or small groups with the information or graph in the centre of a large piece of paper and then write their own questions around it, or use as a whole-class activity to pool ideas. Younger children could be given a photograph to use instead of a written problem, such as a picture of a plate of biscuits or prices of items at a shop, and asked about what they can see. The teacher could scribe their ideas and start to formulate possible questions with them. Pupils could then sort their questions in different ways – perhaps by calculation type, by the number of steps involved, by questions with similar structures or ones where they must use known facts.
Once pupils have explored the possible questions that can and cannot be solved from the given information, the actual question can then be revealed. Frequently, this is a question that they have already considered but, because they have investigated different possibilities rather than a specific goal, they have concentrated much more on different problem structures.
So, what has been the impact of using goal free problems?
After regular use, the difference in confidence, resilience and progress is very noticeable. Pupils who struggle because their level of fluency is not secure enough have had the cognitive load reduced significantly; they feel free to explore the problem. ‘Number grabbing’ has been replaced with increased visualisation and thinking about the questions as ‘stories’, resulting in improved comprehension and understanding of the problems. The flexibility in the questions has produced valuable mathematics talk and given opportunities to identify misconceptions in mathematical vocabulary.
Those children who usually solve word problems more easily are taken out of their comfort zone and tasked to write their own questions to fit the information given, and they enjoy the challenge of ‘Can you create the hardest
question you can think of to ask a friend?’ It also means they are less focused on always having the answer first, which can be demotivating for other pupils.
We teach pupils the skills and maths concepts that they need to answer questions but we cannot expect pupils to instinctively know how to solve word problems, so why not have a go at using goal free questions with your class?
